1. Introduction to Piecewise differential operators, Piecewise integral operators, and their properties 2. Applications of Piecewise derivative: Covid-19 model 3. Applications of Piecewise derivative: Lassa fever model4. Applications of Piecewise derivative: Tumor growth model with radiotherapy and chemotherapy treatment5. Applications of Piecewise derivative: Lorenz attractor 6. Applications of Piecewise derivative: Chen-Lee attractor7. Applications of Piecewise derivative: Heart-rhythm model 8. Applications of Piecewise derivative: Heat equation 9. Applications of Piecewise derivative: Unsteady flow in a confined aquifer10. Applications of Piecewise derivative: Telegraph equation 11. Applications of Piecewise derivative: Advection-dispersion equation